Comparison of orientations of stress and strain tensors based on fault plane solutions in Kaoiki, Hawaii

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Abstract
The stress tensor orientation was estimated based on inversion from 238 first motion fault plane solutions of earthquakes with mostly M = 3.5 ± 0.6 located in the 10‐km radius Kaoiki crustal volume. Separate inversions for subvolumes containing 20–50 events yielded the same results in several adjacent volumes, suggesting that the stress tensor is homogeneous in those parts of the Kaoiki area and that the inversion results are stable and meaningful. Five spatial subsets of the data were found for which the orientation of at least one of the principal axes was different from that in the other sets by 20°–80° and at confidence levels exceeding 95%. The volcano summits of Kilauea and Mauna Loa, and their rift systems, are identified as the source of stress in the Kaoiki crust, because the greatest principal stress points to Kilauea and Mauna Loa. In addition, the strain tensor due to energy released by these 238 earthquakes was computed for the Kaoiki area, and several subvolumes of it, by summing the moment tensors. The moment tensor of each earthquake was constructed from the individual fault plane solutions and from an estimate of the scalar moment derived from the moment‐magnitude relationship. A comparison of the directions of strain and stress tensors showed close agreement for subvolumes with predominantly strike‐slip faulting. In these volumes the inversion process for stress directions led to misfits of approximately equal size for the conjugate near vertical nodal planes. These observations are interpreted to show that in the strike‐slip regime of the upper part of the crust, neither of the nodal planes is preferred for faulting. Rupture probably occurs along the NW and along the NH striking nodal planes in separate earthquakes. Subvolumes with more decollement faulting showed significant differences of 30°–40° between the principal strain and stress directions. In these volumes the near‐horizontal nodal planes showed noticeably smaller misfits in the inversion for the stress directions. These facts are interpreted to indicate that the decollement plane is weak, allowing slip on it even if the principal stresses are inclined at a large angle to it. It is proposed that comparison of strain and stress tensor calculations may be able to differentiate between tectonic regimes uniform in strength (no well developed fault plane) and regimes in which a fault with low frictional strength dominates. As a function of time, significant rotations of the strain tensor by approximately 45° can be observed, which seem to be related to the occurrences of Kaoiki mainshocks. During three background periods of about 7 years each, the average strain tensor showed an orientation typical for predominant decollement faulting, while two premainshock periods of 2.5 years each showed an orientation closer to strike‐slip faulting. It is proposed that this pattern may be repeated before the next Kaoiki mainshock. The strain released seismically is less than the geodetically observed strain by approximately an order of magnitude. (Stress, strain, fault plane solutions, Hawaii.)